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Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function

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  • Hu, Guikai
  • Peng, Ping

Abstract

This article investigates the minimaxity of matrix linear estimators of regression coefficient matrix in a general multivariate linear model with a nonnegative definite covariance matrix allowing for relations between the covariance matrix and the design matrix under a balanced loss function. In a subset of all matrix linear estimators, matrix linear minimax estimators are obtained and proved to be unique almost surely on the suitable hypotheses.

Suggested Citation

  • Hu, Guikai & Peng, Ping, 2012. "Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 286-295.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:286-295
    DOI: 10.1016/j.jmva.2012.04.004
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    References listed on IDEAS

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    1. Yu, Sheng-Hua, 2007. "The linear minimax estimator of stochastic regression coefficients and parameters under quadratic loss function," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 54-62, January.
    2. Jafari Jozani, Mohammad & Marchand, Éric & Parsian, Ahmad, 2006. "On estimation with weighted balanced-type loss function," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 773-780, April.
    3. Hu, Guikai & Peng, Ping, 2011. "All admissible linear estimators of a regression coefficient under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1217-1224, September.
    4. Kazuhiro Ohtani & David Giles & Judith Giles, 1997. "The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function," Econometric Reviews, Taylor & Francis Journals, vol. 16(1), pages 119-130.
    5. Tsukuma, Hisayuki, 2009. "Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2296-2304, November.
    6. Tsukuma, Hisayuki, 2008. "Admissibility and minimaxity of Bayes estimators for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2251-2264, November.
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    Cited by:

    1. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2014. "Bayes minimax estimation of the multivariate normal mean vector under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 96-101.

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